Imported OBJ file with transparent texture has black background
Edit : So my answer only answers partially to your problem, whoever knows a bit better about Obj and Mtl imports will hopefully give you a better answer.
I don't know how to work without nodes, so I show you the problem and the solution with the nodes:

You want your arrow to show up on your object on a red background, here is the current node organization:



This node organization doesn't allow you to show any background, so it shows only black where there's the alpha transparency. The red you see in Solid mode is actually the color you've picked as Viewport Display color:



To create a red background, you have several solutions, you can plug your Image Texure into a MixRGB, choose a red color in the second socket, and plug the Image Texture alpha output into the factor of the MixRGB: